Is there an add-on for a knife-like tool for curves?
No there is not. Unfortunately there are very few cad-like tools for bezier curves in blender. Curves are kind of a second-class citizen, and although they have improved considerably in recent years, they are still not regarded as primary modeling tool.

The closest I know you could currently get is probably a relatively recent addon "Extend / Trim Curve CAD Tools for Bezier Splines" which works relatively well for most situations:
http://blenderartists.org/forum/showthread.php?387520-Addon-Extend-Trim-Curve-CAD-Tools-for-Bezier-Splines